Question

4) Suppose there is a 3-year bond with a $1000 face value, 30% annual coupon payments and a 20% annual yield to maturity. a) Without any calculation, briefly explain whether this bond will be selling a premium or a discount b) Calculate the price of this bond. c Calculate the duration of this bond. d) Suppose the interest rates in the economy rise by 5 percentage points immediately after someone bought this bond. Show a calculation using duration for what should happen to the price of this bond immediately. Suppose now one year passes and the interest rates in the economy are still 5 percentage points higher. If the person that owns this bond sells it for fair value, what would be their one year rate of return? Show a calculation. e) 5 For each of the following state whether it is True or False and provide a brief explanation (I or 2 sentences) as to why it is true or false. a) b) c) All else the same, a higher coupon rate will mean a higher price for a standard coupon bond. All else the same, a higher coupon rate will mean a higher duration for a standard coupon bond. All else the same, a shortage in the money market will lead to the price of bonds falling.

Answer 1

a) since here the coupon payment is higher than yield to maturity the bond is selling at premiun
b)price of bond can be found uisng below formulae
Price=(coupon*(1-((1+i)^-n))/i)+(issue price*(1+i)^-n)
Coupon=face value*coupon rate
=1000*30%=300
i=20%
n=3 years
issue price=1000
substituting in formuale we get it as 1210.65
c)duration of bond below

Inputs Rate Convention: 1 EAR, 0 APR Annual Coupon Rate (CR) Yield to Maturity (Annualized) (y) Number of Pavments/ Year (NOP Number of Periods to Maturity Face Value (F 0 30.00% 20.00% 3 $1,000 Outputs Discount Rate Period (RATE) Coupon Payment (PMT) 20.0% $300 Calculate Bond Duration using the Cash Flows Period Time (Y ears Cash Flows Present Value of Cash Flow Weight Weight * Time Maculay Duration Modified Duration 0 3 3.0 3 3.0 0.0 2.0 Total $300.00$300.00 $300.00 $1,000.00 $1,900.00 $250.00 $208.33 $173.61 $578.70 $1,210.65 20.6501% 17.2084% 14.3403% 47.8011% 100.0% $2.41 0.207 0.344 0.430 1.434 2.41 2.01

Maculay duration 2.41 years

BOND DURATION Basics 3 Inputs 4 Rate Convention 1 EAR, 0 APR 5 Annual Coupon Rate (CR) 6 Yield to Maturity (Annualized) (y) 7 Number of Payments Year ( 8 Number of Periods to Maturity (T) 9 Face Value (FV) 10 11 Outputs 12 Discount Rate /Period (RATE 13 Coupon Payment (PMT) 1000 15 Calculate Bond Duration using the Cash Flows 16 Period 17 Time (Years 18 Cash Flows 19 Present Value of Cash Flow 20 Weight 21 Weight Time 22 Maculay Duration 23 Moditied Duration -B16/NOP -C16/NOP PMT =C18/((1 + RATE)"C16) -C19/SGS19 C20 C17 -D16/NOP -E16/NOP PMT モ18/K1 + RATE)"E16) モ19/SG$19 -F16/NOP 1000 :F18/((1+RATEYF16)|=SUM(C19:F19) -F19/SGS19 :F20"F17 Total PMT =D18/((1+RATErD16) -D19/SG$19 D20 D17 -SUM C18 F18) G19/SG$19 SUM(C21 F21) 20'E 1 7 -SUM C21:F21) -B22(1+RATE

d)the price of bond will come down since here the interest rate increased. Since the price and yield are inversely proportional to each other
Bond Price Change=(Duration×Yield Change*100)
=-2.41*5%=-12.05%

e)let us find price of bond after one year
Price=(coupon*(1-((1+i)^-n))/i)+(issue price*(1+i)^-n)
Coupon=face value*coupon rate
=1000*30%=300
i=25%
n=2 years
issue price=1000
substituting in formuale we get it as 1072
return=(final/initial)-1
=(1072/1210.65)-1=-11.45%